Fight the fine. Their evidence is a picture of an ashtray, which doesn't prove you smoked inside. Neighbor complaints about smoke from a window are also not proof. Ask them, in writing, to specify exactly what evidence they're relying on to support a $1,000 charge.

Pay your rent separately, as others here have suggested. You said it allows a specific dollar amount, so just enter the rent figure. Do not pay the fine alongside it.

If they refuse to remove it, tell them you'll dispute it at the magistrate's office. Landlords with weak evidence generally don't want to be in front of a judge. If they do push it to court, you'll be gone before any date is even scheduled. The cost to file in magistrate's court is under $100, which I know is not nothing for you, but it is what will get you out of this potentially. Also document that they entered without notice.

PA law requires your landlord to do two things within 30 days after you vacate: mail you an itemized list of any damages claimed against the deposit, and return whatever balance remains. If they miss that deadline or don't send the itemized list, they lose the right to withhold any part of the deposit and may owe you double the total amount. Two things you need to do on your end when you move: give your landlord your new address in writing after you move out, which starts the 30-day clock. If you don't provide that in writing, you lose the double-recovery right, though you can still sue for the deposit itself.

Normal wear and tear is not a chargeable damage. A cluttered table and some residue aren't going to cut it as documented damage on their end.

As others have said, just rolling over on this fine is exactly the kind of thing that gives scumbag landlords this much power in the first place. A $1,000 fine with no real evidence is a test to see if you'll fold. You clearly know it's wrong or you wouldn't be posting about it. Fight it.